Why is Athene's core on some casters but not
others?

My name in LoL is "Toyz" and I played Anivia in the world championship finals against Azubu Frost. My build was Athene's / Sorc / Deathcap / QSS / Void Staff.

ROA is a great item for Anivia, but I wouldn't call it "core" -- Athene's edges it out. It's still a key pick depending on the matchup if your opponents have un-counterable initiates and you flat-out need the raw HP (and do not need Athene's MR so much), etc. So it's situational, but Athene's you will always want on Anivia, IMO.